Geodesic
Periodic solutions for functional differential equations with periodic delay close to zero
Electronic journal of differential equations, Tome 2006 (2006)
This paper studies the existence of periodic solutions to the delay differential equation

$ \dot{x}(t)=f(x(t-\mu\tau(t)),\epsilon)\,. $

The analysis is based on a perturbation method previously used for retarded differential equations with constant delay. By transforming the studied equation into a perturbed non-autonomous ordinary equation and using a bifurcation result and the Poincare procedure for this last equation, we prove the existence of a branch of periodic solutions, for the periodic delay equation, bifurcating from $\mu=0$.
Classification : 34K13
Keywords: differential equation, periodic delay, bifurcation, h-asymptotic stability, periodic solution 
@article{EJDE_2006__2006__a62,
     author = {Hbid,  My Lhassan and Qesmi,  Redouane},
     title = {Periodic solutions for functional differential equations with periodic delay close to zero},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1118.34056},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a62/}
}
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Hbid,  My Lhassan; Qesmi,  Redouane. Periodic solutions for functional differential equations with periodic delay close to zero. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a62/